Binding energy and wave function of the alpha-particle ground state

The binding energy problem for the alpha particle is considered using an orthonormal classification of the ground state wave functions and an interaction potential represented by a superposition of the two-body Hamada--Johnston potentials for the six nucleon pairs. Matrices for energy terms of the alpha particle and a matrix for the ground-state wave function are determined in a 32-dimensional spin--isospin space. The 6-dimensional phase-space integrals are solved by the Monte Carlo method. In first approximation, the wave function is assumed to consist of a principal S-state wave function and one of five D-state wave functions. The radial parts of the wave functions are assumed Gaussian. The boundary condition on the wave function at the hard core radius, r/sub c/, is satisfied by introduction of a continuous correlation function which is zero inside the hard core, quadratic in the ''adjustment'' region, (r/sub c/, r/sub c/ + d), characterized by a ''healing'' distance d and l for an interparticle distance beyond r/sub c/ + d. For the model, in which we neglect the effect of the spin--orbit coupling term and the quadratic spin--orbit term in the energy balance and in which we do not account for the repulsive Coulomb interaction, calculations yield a minimum internal energy for the alpha particle of (31.68 +- 2.69) MeV. After a modification of the Hamada--Johnston potential, by reducing the critical radius, r/sub c/, to 0.385 fm (slightly more than 20 percent lower value than the one suggested by Hamada and Johnston), the minimum total energy for the chosen model is (-25.09 +- 3.00) MeV. This result can be compared with the well-known experimental value of 28.296 MeV for the alpha particle binding energy. (Diss. Abstr. Int., B.)